program slows exponentially

Hi,

My problem is that my Java program runs too slowly, and in a way that I don’
t understand.  What I have written is a simulator that models a chemical rea
ction.  
The code seems to work ok, giving the kind of output I expect.  As part of t
he input parameters I specify the “size” of the system that is reacting.  Fo
r a very small system, this runs to completion within a few minutes on a  PC
, which is fine.  However, as soon as I increase the system size, the execut
ion time increases exponentially, in the sense that doubling the system size
 increases the execution time by far more than a factor of 2.  This causes t
he problem that, for a system size big enough to give a useful output, the e
xecution time quickly ramps nastily.  

I realise that any code (including mine) could be optimised for speed, given
 enough time and attention.   But I wondered if the symptoms of “exponential
 slowing” that I’m finding are a pointer to something else other than code i
nefficiency being the problem.

Any suggestions?